2025/26 AHSMC Part 1 Problem 2

Problem 2 of 16

Two solid iron right circular cylinders are each $4$ cm high, and are of diameter $60$ cm and $25$ cm respectively. They are melted down and used to form a single larger right circular cylinder, still $4$ cm high. What is the diameter in cm of the newly created larger cylinder?

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Solution

The volumes of the two cylinders are $V_1 = 60^2\pi$ and $V_2 = 25^2\pi$ (the height $4$ cancels against the factor $4\cdot(D/2)^2$ ). If $D$ is the new diameter then $D^2 = 60^2 + 25^2 = 5^2(12^2 + 5^2) = 5^2 \cdot 13^2 = 65^2$ , so $D = 65$ . The answer is (A).

University of Alberta

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